#2**+1 **

There is no methodical reasoning behind five-digit perfect square palindromes. It's a matter of squaring all the numbers from 100 to 316.

(317^{2} = 100489)

101^{2} = 10201

111^{2} = 12321

121^{2} = 14621

202^{2} = 40804

212^{2} = 44944

264^{2} = 69696

307^{2} = 94249

For four-digit perfect square plaindromes... there are none!

So, your answer would be the 7 five-digit perfect square palindromes that we stated above.

mathleteig Nov 9, 2019